The characteristic x-ray emission direction of a material indicates the direction of the bonding orbitals and spatial symmetry of the electron orbitals. Accordingly, the intensity of x-ray emission, which varies with the direction of emission and crystal orientation, provides crucial information regarding anisotropic electronic structures. This study utilized angle-resolved soft x-ray emission spectroscopy (SXES) on a layered material, NaAlSi, to ascertain the spatial distribution of the valence electrons. Distinct alterations in the spectral intensity distributions were observed in the Al–L2,3 and Si–L2,3 spectra with respect to the emission angle. To interpret the anisotropic SXES spectra, the spatial distribution of each valence electronic state was simulated using first-principle calculations. Although the anisotropic emission intensity could not explain the symmetry of the spatial distributions of the isolated s and d atomic orbitals, the anisotropy of the SXES spectra could be interpreted as the spatial distribution of these orbitals when hybridized with p orbitals. Furthermore, the spectral structure corresponding to the electronic states near the Fermi level reflected the characteristics of the d orbitals. Therefore, angle-resolved SXES measurements can effectively discern the spatial distribution of hybridized electron orbitals with specific energy levels, which could enhance techniques related to electron distribution analysis, with potential applications in material science and electronic structure characterization.

Spectroscopic measurement methods employing electron microscopes are vital for probing the electronic structure in local regions beyond the microscale. Among these analytical methods, soft x-ray emission spectroscopy (SXES) conducted with electron microscopes has not only permitted the elemental analysis of materials but also facilitated the analysis of the occupied bonding states.1–3 Additionally, the SXES technique based on electron microscopy has enabled the visualization of the spatial distribution of chemical bond states in materials with locally inhomogeneous electronic structures.4,5 On the other hand, the direction of the x-ray emission is influenced by the bonding direction and atomic orbital symmetry surrounding the atomic core.6 In SXES measurements utilizing synchrotron radiation as well as electron microscopy, the intensity of x-ray emission is reportedly dependent on the crystal orientation with anisotropic structures, such as graphite,7,8 h–BN,9 and hexagonal closed-packed metals.10 However, angle-resolved SXES measurements have only been applied in certain studies to delineate the electronic structures of functional materials.

NaAlSi possesses an anti-PbFCl-type layered structure in the space group of P4/nmm11 and has garnered considerable research interest as a topological semimetal. The electronic structure of NaAlSi has been examined through first-principle calculations, where hybridization between the Al–s and Si–p orbitals resulted in the formation of a nodal-line band near the Fermi level, indicative of a topological semimetal.12–15 The band structure near the Fermi level was observed through photoelectron spectroscopy measurements, including nodal-line band dispersion.16 However, the electronic structure of the entire valence band of NaAlSi has not been thoroughly investigated. Kuroiwa et al. identified the superconductivity of NaAlSi at Tc = 7 K for polycrystalline materials prepared under high pressure.17 Schoop reported the superconductivity at Tc = 9 K under 2 GPa but disappeared at 4.8 GPa.18 Thereafter, the synthesis of mm-size single crystals through the Na–Ga flux method was presented, where the superconductivity of the NaAlSi was observed at Tc = 6.8 K under atmospheric pressure.19 The anisotropic electrical resistivity of NaAlSi was further elucidated by electrical conductivity measurements, which illustrated the T2 dependence of the electrical resistance, highlighting that the electronic correlations influence the electrical conductivity.19 

The crystal structure of NaAlSi is depicted in Fig. 1, wherein the layered structures of Na and Al–Si bonds are constructed. In the Al–Si layer, each Al atom is encircled by four Si atoms, forming a tetrahedral arrangement. Because the Al atom receives an electron from Na to constitute a four-electron configuration, it is predicted to establish an electronic structure grounded in sp3 hybridization with the neighboring Si atoms. Conversely, an anisotropic electronic structure may be formed because of the layered structure that contains Al and Si atoms. Examining the anisotropy within the electronic structure of the Al–Si layer is essential for comprehending the electronic attributes of NaAlSi, specifically as the electronic structure near the Fermi level is composed of Al-s and Si-p orbitals, in accordance with theoretical calculations.12–15 

FIG. 1.

Crystal structure of NaAlSi.10 

FIG. 1.

Crystal structure of NaAlSi.10 

Close modal

The dependence of the x-ray emission intensity on the crystal orientation in NaAlSi may provide insights into whether the valence electron orbitals of Al and Si atoms are characterized by sp3-hybridization or whether they form an anisotropic electronic structure owing to the layered structure. In the present study, angle-resolved SXES measurements were performed on single-crystal NaAlSi to examine the electronic structure within the valence band of NaAlSi. To facilitate angle-resolved SXES measurements, we fabricated a sample-tilting stage for the electron probe microanalyzer (EPMA). Moreover, the emission angle dependence of the spectral intensity distribution was comparatively analyzed with the theoretical density of states (DOS) derived from first-principles calculations, and the anisotropic electronic structure was examined.

For the SXES measurement, the EPMA (JXA-8230, JEOL) attached to an SXES spectrometer (SS-9800 SXES, JEOL)20 was operated at 5 kV with a probe current of 5 × 10−8 A and probe size (diameter) of approximately 0.5 μm. According to Castaing’s equation,21 the diameter of x-ray generation volume of NaAlSi at an acceleration voltage of 5 kV is estimated to be approximately 500 nm for Al–L and Si–L, which should reflect valence electronic states as bulk. In this experiment, a varied-line-spacing grating featuring an average groove density of 1200 lines/mm (JS200 N) was employed for the 52–213 eV range. The energy resolution of the spectrometer is 0.1 eV for Al–L2,3. The total acquisition period for each spectrum was recorded for 10 min. The sample stage was designed to tilt the specimen ±30° from the horizontal, as shown in Figs. 2(a) and 2(b). A stepping motor served as the tilt drive source, enabling control with a 0.2° tilt increment per step. Given that the x-ray emission spectrometer was positioned 40° upward from the horizontal, the angle of the x-ray emission spectra ranged between 10° and 70°. Furthermore, the stage could be manually rotated in alignment with the normal axis.

FIG. 2.

(a) Image of the specimen tilting holder for the EPMA instrument. (b) Angle region for SXES measurements. (c) SEM image of NaAlSi. Facet plane indicated by the dashed line corresponds to the (100) plane of the NaAlSi single crystal, as confirmed by EBSD.

FIG. 2.

(a) Image of the specimen tilting holder for the EPMA instrument. (b) Angle region for SXES measurements. (c) SEM image of NaAlSi. Facet plane indicated by the dashed line corresponds to the (100) plane of the NaAlSi single crystal, as confirmed by EBSD.

Close modal

The crystal segments of NaAlSi were synthesized by Na–Ga flux method.19 The crystal segments were single crystals with a few mm in size. The crystal orientation of NaAlSi was ascertained by analyzing the backscattered electron diffraction (EBSD) patterns using scanning electron microscopy (SEM, JSM-7800F, JEOL). Figure 2(c) shows an SEM image of NaAlSi, where a facet denoted by a dashed line corresponds to the (100) plane. The coarse surface visible at the center of Fig. 2(c) resulted from oxidation. The SXES spectra were acquired at room temperature from a flat top surface, denoted as (001), marked by a dotted-square line in Fig. 2(c), which is expected to exhibit reduced surface oxidation. In the specimen stage, the [100] direction, perpendicular to the (100) plane of NaAlSi, was oriented toward the horizontal SXES detection side. In other words, the x-ray emission intensity was examined for the emission direction in the ac-plane of the NaAlSi crystal.

Simulations of the electronic structure of NaAlSi were performed using the full-potential linearized augmented plane wave method22 within WIEN2k.23 The exchange-correlation function was applied using the generalized-gradient approximation as formulated by Perdew, Burke, and Ernzerhof.24 The convergence condition for the self-consistent cycle calculation was established at a cut-off energy of 0.0001 Ry, force of 0.001 Ry/au, and charge of 0.001 e. The k-mesh for the calculation was designated 10 000 points. The parameters of the crystal structure of NaAlSi were obtained from the literature.11 

Figure 3 illustrates (a) the Al–L2,3 and (b) Si–L2,3 emission spectra of NaAlSi within the energy ranges of 60–75 eV and 85–100 eV, respectively. These spectral intensity profiles indicate the partial DOS of the valence band (VB) with s and d symmetries. The computational result of DOS of s and d components for Al, Si, and Na elements is also shown in Fig. 3(c). The spectra were acquired for an emission direction of 40°, defined with respect to the a-axis toward the c-axis of the NaAlSi crystal. The Al–L2,3 spectrum showed a steep increase in the intensity with a 0.1 eV increase in the width equivalent to the energy resolution as shown in the inset in Fig. 3(a). This spectral intensity distribution corresponds to the DOS structure at the Fermi level of the metal. The energy position of the Fermi level of NaAlSi for Al–L2,3 was determined at 73.4 eV, which corresponds to the middle point of the intensity increase width. On the other hand, the onset of Si–L2,3 was observed at 98.8 eV, where the spectral intensity distribution showed a gradual increase in the intensity, rather than a steep change in the intensity characteristic of a metal. As shown in Fig. 3(c), the s and d components of the DOS for Si are very weak and a gradual increase in the intensity of DOS was reproduced near the Fermi level. Therefore, the position at 98.8 eV, where the spectral intensity of the Si–L2,3 begins to increase, was assigned as the Fermi level. In Fig. 3, both Al–L2,3 and Si–L2,3 spectra are depicted and aligned at the Fermi level (EF) for Al–L2,3 and the highest energy state of the VB for Si–L2,3. The energy positions of the spectral peaks and structures in the two spectra were nearly identical to one another, indicating that the VB consisted of the hybridized constituents of Al and Si. The formation of hybridized orbitals between Al and Si is evident from the fact that the DOS structures of the Al and Si components in Fig. 3(c) are found at the same energy positions. The DOS components of Al and Si are more dominant than that of Na, indicating that Al–L2,3 and Si–L2,3 reflect the main electronic structure of the valence band of NaAlSi.

FIG. 3.

(a) SXES spectra of Al–L2,3 and Si–L2,3 in NaAlSi. (b) Al–L2,3 and Si–L2,3 spectra aligned at the Fermi level. (c) Calculated DOSs of s and d orbitals for Al, Si, and Na.

FIG. 3.

(a) SXES spectra of Al–L2,3 and Si–L2,3 in NaAlSi. (b) Al–L2,3 and Si–L2,3 spectra aligned at the Fermi level. (c) Calculated DOSs of s and d orbitals for Al, Si, and Na.

Close modal

Figure 4 depicts the emission angle dependence of both the (a) Al–L2,3 and (b) Si–L2,3 spectra. These emission angles, in relation to the a-axis, ranged from 20° to 70°, advancing in increments of 10°. Spectral intensities were normalized to the intensity integrated over the ranges of 58–75 eV for Al–L2,3 and 75–100 eV for Si–L2,3. The spectral intensity varied with the emission angles. The spectral structures, designated as A–D, demonstrated a fluctuation in the emission intensity, where structures A–C were common for Al– and Si–L2,3 and structure D was common only for Al–L2,3. Within the Al–L2,3 spectra, spectral structure C exhibited an increase in the intensity corresponding to the emission angle, whereas structure B exhibited no significant variations in the intensity. As the emission angle increased, the intensity of D increased, peaking at 40° before declining with a further increase in the emission angle. Structures A and C for Si–L2,3 suggested a pertinent intensity increase with the increase in emission angles, implying that x-ray emission in the c-axis direction is relatively more potent than that in other directions. The anisotropic characteristics of the SXES spectra can be attributed to the orientation of the electron orbitals. To further analyze the symmetry component potentially contributing to each spectral structure, DOS simulations for each orbital were conducted using WIEN2k.

FIG. 4.

Emission angle dependence of (a) Al–L2,3 and (b) Si–L2,3. The emission angles in terms of the a-axis ranged from 20° to 70°, with an angle step of 10°. Spectral intensity distribution is magnified in spectra i–iv.

FIG. 4.

Emission angle dependence of (a) Al–L2,3 and (b) Si–L2,3. The emission angles in terms of the a-axis ranged from 20° to 70°, with an angle step of 10°. Spectral intensity distribution is magnified in spectra i–iv.

Close modal

Figure 5 presents the computational results of the DOS for the 3s, 3p, and 3d symmetries of Al and Si within the NaAlSi. Zero energy on the lateral axis corresponds to the EF position. The s- and p-orbital components were prominent, whereas the d-orbital components were minor within the DOS. Owing to the dipole selection rule, the Al–L2,3 and Si–L2,3 spectra should be comparatively assessed with respect to the DOS of s and d orbitals. The dashed vertical lines labeled A–D in Fig. 5 are analogous to the spectral structures labeled A–D in Fig. 4. The energy positions of spectral structures A–D from EF closely align with the DOS structures at −8, −5.5, −4, and −1 eV, respectively.

FIG. 5.

Calculated density of states of Al and Si in NaAlSi.

FIG. 5.

Calculated density of states of Al and Si in NaAlSi.

Close modal

To elucidate the anisotropic characteristics of the Al– and Si–L2,3 spectra, the orientations of the d orbitals must be considered, as each d-orbital component possesses an anisotropic spatial charge distribution. According to the electromagnetic theory,6 the x-ray emission direction is orthogonal to the accelerating vector of an electron transitioning from the valence to the inner orbitals. Consequently, the predominant emission direction is approximately perpendicular to the spatial dispersion direction of each valence electron orbital. For instance, the spatial distributions of d x y and d x 2 y 2 are distributed in the ab in-plane direction of NaAlSi. Thus, these orbitals are predominantly emitted toward the c-axis direction. As the d y z and d z x orbitals spread in the bc- and ac-planes, respectively, the emission directions were dominant along the a- and b-axes, respectively. The emission from the d 3 z 2 r 2 orbitals should be aligned in the ab in-plane direction. However, as indicated in Table I, where the calculated primary components of the d orbitals and the anticipated emission direction based on the spatial distribution of the d orbitals are depicted, none of the spectral structures can be explained by the spatial distribution of the d orbitals. Furthermore, the DOS components of the d orbitals are substantially smaller than those of the s and p orbitals within the electronic structures of Al and Si. Therefore, the interpretation employing the atomic orbital theory cannot adequately explain the conspicuous directional dependence observed in the experimental x-ray emission intensity.

TABLE I.

Correlation between x-ray emission direction and d orbital.

Cal. Al-d component (Emission direction)Emission direction in EXP. Al–L2,3Cal. Si-d component (Emission direction)Emission direction in EXP. Si–L2,3
dxy (c-axis) No angle dependence Negligible c-axis 
d x 2 y 2 (c-axis) No angle dependence dyz, dzx (ab-plane) c-axis 
dyz, dzx (ab-plane) c-axis dyz, dzx (ab-plane) c-axis 
dxy (c-axis) 40° from a-axis … … 
Cal. Al-d component (Emission direction)Emission direction in EXP. Al–L2,3Cal. Si-d component (Emission direction)Emission direction in EXP. Si–L2,3
dxy (c-axis) No angle dependence Negligible c-axis 
d x 2 y 2 (c-axis) No angle dependence dyz, dzx (ab-plane) c-axis 
dyz, dzx (ab-plane) c-axis dyz, dzx (ab-plane) c-axis 
dxy (c-axis) 40° from a-axis … … 

From the computational results of the DOS, spectral structures A–C were predominantly influenced by the s-orbital components of Al and Si. An isolated s-orbital possessing a distinct orbital energy does not display anisotropic x-ray emission. However, when considering the hybridization of the s-orbital with other orbitals of different energies, the electronic states of the s components within the hybridized orbitals were distributed throughout the VB. In this context, the spatial distribution of the s component within a confined energy range in the VB deviates from spherical symmetry. Consequently, the hybridized s orbital within a limited energy range may exhibit anisotropic x-ray emissions. To verify the relationship between the spatial charge distribution of the hybridized sp orbitals and the x-ray emission direction, simulations were conducted for the charge density distributions corresponding to the energy region of spectral structures A–C. Additionally, the charge density distribution corresponding to spectral structure D of Al–L2,3, incorporating a d-orbital component alongside the s orbital, was simulated.

Figure 6(a) illustrates the four sections of the (i) (400) plane including the Si–Al bond, (ii) (110) plane including the Al–Al bond, (iii) plane on the Al atom layer, and (iv) plane of the Si atom layer for visualizing the charge density distributions. The energy for the charge density distributions ranged across −8.0 to −7.5 eV for A, −5.5 to −5.0 eV for B, −4.3 to −3.8 eV for C, and −1.0 to −0.5 eV for D.

FIG. 6.

(a) Crystal planes (i)–(iv) of the NaAlSi crystal to visualize the charge densities for each energy region. (b) Charge density distribution of NaAlSi in energy regions A–D.

FIG. 6.

(a) Crystal planes (i)–(iv) of the NaAlSi crystal to visualize the charge densities for each energy region. (b) Charge density distribution of NaAlSi in energy regions A–D.

Close modal

Figure 6(b) depicts the spatial charge distribution for each energy range (A–D) and crystal plane [(i)–(iv)]. These spatial charge distributions encompass all components of the electronic orbitals. Within energy region A [Fig. 6(b) A-(i)], the charge density was primarily concentrated around the Si atoms and, to a lesser extent, around the Al atoms. This computational result is consistent with the more pronounced intensity of A in Si–L2,3 compared to Al–L2,3. Although the charge distribution surrounding the Si atoms was largely isotropic, closer inspection revealed a slight distortion toward the Al atoms. The experimental emission intensity of structure A in Si–L2,3 is more driven toward the c-axis, indicating that the lateral component of the charge density distribution has intensified owing to the distortion in the Al direction. In energy region B [Fig. 6(b) B-(i)], the charge density was distributed between the Al and Si atoms, indicating the formation of a sp3σ bond. As shown in Fig. 4, spectral structure B does not show a clear change in the intensity for both Al– and Si–L2,3. This isotropic emission can be explained by the fact that the emission from the four sp3–σ bonding orbitals extending toward the tetrahedral apex shows an overall isotropic emission intensity.

The charge density adjacent to the Al atomic core in the energy range C [Fig. 6(b) C-(i), (ii)] circulates in the lateral direction of the atomic core. This distribution is in agreement with the experimental anisotropic feature of the structure C of Al–L2,3, where the emission intensity was observed to be higher in the c-axis direction [Figs. 4(a)4(i)]. In contrast, the charge density surrounding the Si atoms in this energy region manifests in a hemispherical pattern [Fig. 6(b) C-(i)]. The charge density along the c-axis direction should be less compared to that in the case of a spherical charge distribution. Consequently, the emission intensity in the ab in-plane direction is likely to be reduced in comparison with that in the case of a spherical charge distribution. The spectral structure C of Si–L2,3 exhibited a stronger emission intensity toward the c-axis as opposed to the a-axis direction, which is consistent with the calculated spatial charge distribution.

In energy region D [Fig. 6 D-(i)], the charge density surrounding the Al atoms is inferior to that around the Si atoms; however, the spectral intensity is predominantly influenced in Al–L2,3 by the s and d components. The empirical observation that the intensity of the spectral structure D of Al–L2,3 did not follow a monotonic increase or decrease with an increase in the emission angle but rather attained a maximum at 40° may suggest a characteristic of d symmetry. Figure 6 D-(ii) illustrates that the charge density is distributed above and below the Al atomic plane, corresponding to the π bond of the d z x ( d y z ) orbital. This distribution of the π-bond charge likely elucidates the anisotropy found in the spectral structure D. Within the identical energy region, the d x y component is also present, as shown in Fig. 5(c). In Fig. 4, the spectral structure directed toward the c-axis (emission angles: 60°, 70°) emanating from the d x y orbital was not exhibited as a peak structure but rather as a weak bump structure. This suggests that the bandwidth of the d x y orbital is more expansive than that of the d y z and d z x components, signifying a robust interaction with neighboring electronic orbitals in the ab in-plane direction. Thus, the anisotropy of spectral structure D can be elucidated by the hybridized d-orbital components.

Upon comparing the anisotropy of the SXES spectral intensities with the simulated charge density, the anisotropic emission intensities of Si– and Al–L2,3 could be approximated by considering the distribution of the hybridized s and d orbitals. The analysis of the anisotropy of each spectral structure revealed that valence electrons surrounding Si and Al in NaAlSi comprise not only the sp3-hybridized orbital but also a charge distribution along the ab in-plane direction, thereby denoting a two-dimensional attribute of the electronic structure. Additionally, the angle-dependent nature of the x-ray emission intensity further disclosed the feature of the d symmetry in energy region D, aligned with the electronic states near the Fermi level. Consequently, we can conclude that the electronic characteristics of NaAlSi are affected not only by free-electron-like s and p orbitals but also by the exchange-correlation effects within the d-electron orbitals, as substantiated by the electric resistance experiment.19 The empirical findings of this study indicate that the electronic properties of NaAlSi are influenced by the d-orbital component in the band structure near the Fermi level.

In this study, angle-resolved SXES measurements were performed to analyze the layered crystal structure of NaAlSi. Both the Al– and Si–L2,3 spectra revealed a dependency on the emission angle with respect to the distribution of the spectral intensity. This dependence of the x-ray intensity on the emission direction can be interpreted as an approximate reflection of the valence charge distribution pertaining to the Si and Al atoms. The bonding states interconnecting the Al and Si atoms were formulated based on the sp3 hybridized orbital as well as electron distribution on the Al–Al layer. Moreover, the angle-dependent nature of the emission intensity has diverse characteristics that were consistent with the d-orbital symmetry. Therefore, the angular dependence of the L emission intensity can be interpreted as an anisotropic spatial distribution of the hybridized s and d orbitals.

At present, the analysis of the anisotropic spectral intensity distribution is only qualitative, but if quantitative interpretation becomes possible in the future, we can expect to be able to reconstruct the spatial distribution of electron orbitals from anisotropic SXES data. In addition, electron-microscopy based SXES spectroscopy is a useful analytical technique for elucidating the electronic structure from the assigned specimen area of newly functional materials, which have not been established with the synthesis method of a macroscopic scale single crystal without impurities and crystal defects.

The authors thank Mr. Yasuhiro Suzuki of IMRAM, Tohoku University for fabricating the specimen tilting stage for EPMA. The authors thank Mr. Hideyuki Magara of IMRAM, Tohoku University, for his support in the EBSD experiment. This work was partially supported by JSPS KAKENHI Grant No. 22H00267.

The authors have no conflicts to disclose.

Ryogo Ebisu: Formal analysis (lead); Investigation (lead). Yohei K. Sato: Formal analysis (supporting); Writing – original draft (lead); Writing – review & editing (equal). Takahiro Yamada: Resources (lead). Masami Terauchi: Conceptualization (lead); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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